Introduction
Electric power is typically generated at a generating station or facility, usually at a remote location from a load, and transported to consumers over a transmission and distribution system. To reduce power transportation losses, a step-up generator transformer at the generating station, is used to increase the voltage and reduce the current, for transmission over the transmission system en route to transmission substations. At the transmission substation, step-down transformers are used, to decrease the voltage for sub-transmission or distribution, depending on the area serviced by an electric utility. The electric power is then finally transported to the distribution substation. At the distribution substation, distribution transformers, which are part of the electric utility's secondary power distribution system, reduce the voltage from the transmission or sub-transmission level to a distribution voltage, for delivery and use by industrial, commercial, and residential consumers. Measurement of power and energy is made at many locations along this chain of generation, transmission, distribution and delivery. This chain is collectively termed an electrical power system. The location at which the measurement is made is termed as a metering point. The part of the electrical power system, prior to the metering point is termed a source, and that part following it a load. The transmission and distribution system may be three-phase, single-phase or a mixture. A single-phase electrical system uses two conductors, while a three-phase system may have three or four conductors.
The Problem
The major problem presently experienced is measurement of powers, in the presence of harmonics and non-linear loads, in the electrical power system. The method of determination of powers also contributes to the problem. Non-linear loads have a detrimental effect on components of the power system. These give rise to harmonic power flows to other users of the supply, and contribute to a deterioration of the supply quality. In such a scenario, there is a problem experienced with accurate measurement, especially of non-active (or reactive) power. This is one of the quantities used in billing. Evaluation of the quality of the power supply, to enable allocating costs, to those causing deterioration in the power quality, is also very important. To enable this cost allocation, there is a need to identify the polluters. The method or device should indicate degradation in power quality as well as identify the source. Another important area, is mitigation equipment, used for removing unwanted polluting quantities from the power system. The measurement method or apparatus should provide accurate information for such mitigation equipment. Much research has been conducted into this problem and some of the findings are highlighted in the following paragraphs.
Many references for example (Czarnecki, L. S., Orthogonal decomposition of the currents in a 3-phase nonlinear asymmetrical circuit with a nonsinusoidal voltage source, IEEE Transactions on Instrumentation and Measurement, pp 30-34, Vol. 37, Issue 1, March 1988; F. Ghassemi, New Apparent Power and Power Factor with Non-sinusoidal Waveforms, IEEE Power Engineering Society Winter Meeting, 2000, pp 2852-2857 Vol. 4, January 2000; L. M. Tolbert, T. G. Habetler, Comparison of Time Based Nonactive Power Definitions for Active Filtering, Power Electronics Congress CIEP 2000, pp 73-79, October 2000), state that though active power has an accepted definition, there is ambiguity in defining reactive power, and this is mainly because as stated in (R. Fetea, A. Petroianu, Can the Reactive Power be Used?, Proceedings Power Systems Technology, PowerCon 2000, pp 1251-1255, Vol. 3, December 2000), its average over time is zero.
The control philosophy of compensation systems (compensators) is still a major unsolved problem. Proper control philosophy can only be derived, if the definitions of all the components of electric power, under nonsinusoidal conditions, prove to be accurate, and have an interpretation in terms of the load connected, as identified in references (J H Enslin, J D Van Wyk, A New Control Philosophy for Power Electronic Converters as Fictitious Power Compensators, 19th Annual IEEE Conference Power Electronics Specialist Conference, PESC '88, pp 1188-1196, Vol. 2, 11-14 April 1988; J H Enslin, J D Van Wyk, Measurement and Compensation of Fictitious Power Under Nonsinusoidal Voltage and Current Conditions, IEEE Transactions on Instrumentation and Measurement, pp 403-408, Vol. 37 Issue 3, September 1988).
For sinusoidal systems, powers are defined using RMS (root-mean square) quantities. The RMS based quantities, that have conventionally been used to measure electric power, are generally considered to be accurate when power is supplied to the load with a sinusoidal waveform. Adopting this directly to non-sinusoidal systems using RMS values of voltage and current is not satisfactory. This is because RMS is a derived quantity representing the current or voltage based on heating effect. Use of RMS quantity to represent a single frequency sinusoidal signal is acceptable because the frequency information is not lost, the single frequency being known. However, when a multi-frequency non-sinusoidal signal is represented with a single RMS quantity, the frequency information is lost. Additionally, the characteristics of the load are not wholly of “heating” nature, and this leads to error especially in the measurement of non-active or reactive power.
Many researchers have pointed out issues with current definitions and techniques for measuring electrical power, especially ‘reactive power’, under nonsinusoidal conditions. The IEEE Working group (IEEE Working Group on Nonsinusoidal Situations: Effects on Meter Performance and Definitions of Power, Practical Definitions for Powers in Systems with Unbalanced Loads: A Discussion, IEEE Transactions on Power Delivery, pp 79-101, Vol. 11 Issue 1, January 1996) indicates that present definitions are not adequate for economic studies in nonsinusoidal and/or unbalanced and/or non-linear systems. Strong practical reasons are pointed out in (F. Ghassemi, What is Wrong with Electric Power Theory and How It Should be Modified, Metering and Tariffs for Energy Supply, Conference Publication No 462, pp 109-114, May 1999) for reviewing power definitions. The author in (L. S. Czarnecki, New Power Theory of the 3-Phase Non-linear Asymmetrical Circuits Supplied from Nonsinusoidal Voltage Sources, IEEE International Symposium on Circuits and Systems, pp 1627-1630, Vol. 2, June 1988) states that there is not a power theory that explains the power properties of three-phase-asymmetrical systems under non-sinusoidal conditions. Reference (Institute of Electrical and Electronic Engineers, IEEE Standard 1459-2000—IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions, IEEE, New York, 2000) states of the need for a generalised power theory that can provide simultaneous common base for energy billing, evaluation of electric energy quality, detection of major sources of waveform distortion, and provide information for design of mitigation equipment.
Hartman (D. P. Hartman, An Electrical Utility's Experience with Nonsinusoidal Waveforms and Electrical Metering, IEEE Tutorial Course, pp 23-24, 1990) and Stevens (R. H. Stevens, Harmonics and Related Factors Affecting Metering Accuracy, IEEE Tutorial Course, pp 61-66, 1990) state that the accuracy of electricity meters is affected by nonsinusoidal waveforms. Some definitions, as the following references indicate, do not posses attributes that are related to power phenomena in circuits or the load properties (L. S. Czarnecki, Considerations on the Reactive Power in Nonsinusoidal Situations, IEEE Transactions on Instrumentation and Measurement, pp 399-404, Vol. IM-34, September 1985; L. S. Czarnecki, What is Wrong with Budeanu Concept of Reactive and Distortion Power and Why It Should be Abandoned, IEEE Transactions on Instrumentation and Measurement, pp 834-837, Vol. IM-36, September 1987; L. S. Czarnecki, On Some Misinterpretations of the Instantaneous Reactive Power p-q Theory, IEEE Transactions on Power Electronics, pp 828-836, Vol. 19, No 3, May 2004).
The presence of a source impedance, also causes inconsistent results because source impedance is neglected in definitions, as identified by (R. Sasdelli, Compensable Power for Electrical Systems in Nonsinusoidal Conditions, IEEE Transactions on Instrumentation and Measurement, pp 592-598, Vol. 43 No. 4, August 1994; A P J Rens, P H Swart, Investigating the validity of the Czarnecki three-phase power definitions, Africon Conference in Africa, 6th IEEE Africon, pp 815-821, Vol. 2, October 2002). References (J H C Pretorius et al, An Evaluation of Some Alternative Methods of Power Resolution in a Large Industrial Plant, IEEE Transactions on Power Delivery, pp 1052-1059, Vol. 15 Issue 3, July 2000; L. M. Tolbert, T. G. Habetler, Comparison of Time Based Nonactive Power Definitions for Active Filtering, Power Electronics Congress CIEP 2000, pp 73-79, October 2000) indicate that further confusion is added, because the different definitions diverge and emphasize different qualities suited to different applications. Definitions based on time-domain and frequency domain analysis do not fully agree, as pointed out in (F. Ghassemi, New Concept in AC Power Theory, IEEE Proceedings Generation, Transmission and Distribution, pp 417-424, Vol. 147 Issue 6, November 2000). References (P. S. Filipski, Polyphase Apparent Power and Power Factor Under Distorted Waveform Conditions, IEEE Transactions on Power Delivery, pp 1161-1165, Vol. 6 Issue 3, July 1991; L. S. Czarnecki, Power related phenomena in three-phase unbalanced systems, IEEE Transactions on Power Delivery, pp 1168-1176, Vol. 10, Issue 3, July 1995; Hyusong Kim et al, Spectral Analysis of Instantaneous Powers in Single-Phase and Three-Phase Systems with the use of p-q-r Theory, IEEE 32nd Annual Power Electronics Specialist Conference, PESC 2001, pp 54-61, Vol. 1, 17-21 June 2001) point out that definitions for single-phase systems become ambiguous and controversial for three-phase, non-sinusoidal and non-linear systems.
It is therefore an object of the invention to provide, a method and apparatus that gives time-domain and average measurement of the defined active and non-active power components, which enables cost allocation, and billing of power and energy transfer, at the measuring point.
It is another object of the invention to provide, a method and apparatus that gives time-domain and average measurement of the defined active and non-active power components, which enables identification of the source of pollution of power at the measuring point.
It is another object of the invention to provide, a method and apparatus that gives time-domain and average measurement of the defined active and non-active power components, which indicates degradation of power quality at the measuring point.
It is another object of the invention to enable allocating costs, having identified the polluters and degradation in power quality, to those causing deterioration in the power quality.
It is another object of the invention to provide a method and apparatus, that gives time-domain measurement of the defined active and non-active power and power components, providing information for static mitigating equipment, which enables compensation of unwanted quantities at the metering point.
It is another object of the invention to provide a method that gives time-domain measurement of the defined active and non-active power and power components, in a software based application that enables manual determination of compensation of unwanted quantities, using passive elements (resistors, capacitors and inductors) at the metering point, as well as the objects as stated above.